Oxygen-free methane aromatization has been attracting growing attention due to a potential means for producing high valuable products such as aromatics and hydrogen. Many studies have been focused on catalysts screening and characterization, and elementary thermodynamic steps of the reaction. However, little attention has been paid to fluid dynamics which are important for an industrial application. In the present contribution, COMSOL Multiphysics 4.2 has been used to study the methane dehydroaromatization. First, a fixed catalyst bed reactor is simulated in order to verify the model used, and then coupled with a hydrogen separation membrane. Moreover, the influence of various parameters, such as space velocity, temperature, and hydrogen transport properties, on the reaction, have also been studied.